This dataset accompanies the article "A decomposition method for optimizing the operation of power-to-X energy systems with detailed process models." In the main article, a direct air capture (DAC) plant is modeled at two different levels of granularity: a detailed process model and a corresponding surrogate process model. These models are used to optimize the operational decisions of the DAC plant. The detailed process model of the DAC plant was developed by Postweiler et al. [1] and is formulated as a system of differential-algebraic equations (DAEs). In our work, we treat this model as a black-box model and optimize the operation of a stand-alone DAC plant using the DAE model to achieve a specified CO₂ capture target while minimizing the operational cost. The optimization problems are solved using a particle swarm optimization (PSO) algorithm. The resulting optimization data are collected and provided in this dataset. This dataset includes the following information: Progress of the PSO algorithm Top 1 optimization result Top 10 optimization results More details and instructions can be found in: the accompanying article: https://doi.org/10.1016/j.apenergy.2026.128445 our Git repository: https://git-ce.rwth-aachen.de/ltt/ptg-es4 Please note that the dataset requires approximately 30 GB of storage space. This study is co-funded by the "Europäischer Fonds für regionale Entwicklung" (EFRE-20800350) and the KSB Stiftung Scholarship by the DAAD-Stiftung. The support is gratefully acknowledged. Reference [1] Postweiler, P., et al. Environmental Process Optimisation of an Adsorption-Based Direct Air Carbon Capture and Storage System. Energy & Environmental Science, 17(9), 3004–3020 (2024).